Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, E

Average Accuracy: 44.7% → 46.3%

Time: 34.5s

Precision: binary64

Cost: 27076

\[ \begin{array}{c}[j, k] = \mathsf{sort}([j, k])\\ \end{array} \]

Math

\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

↓

\[\begin{array}{l} \mathbf{if}\;x \leq 10^{-51}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

↓

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 1e-51)
   (-
    (-
     (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
     (* (* x 4.0) i))
    (* (* j 27.0) k))
   (fma
    x
    (fma 18.0 (* t (* y z)) (* i -4.0))
    (fma t (* a -4.0) (fma b c (* k (* j -27.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 1e-51) {
		tmp = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = fma(x, fma(18.0, (t * (y * z)), (i * -4.0)), fma(t, (a * -4.0), fma(b, c, (k * (j * -27.0)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

↓

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 1e-51)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(x, fma(18.0, Float64(t * Float64(y * z)), Float64(i * -4.0)), fma(t, Float64(a * -4.0), fma(b, c, Float64(k * Float64(j * -27.0)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 1e-51], N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision] + N[(b * c + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	44.7%
Target	48.3%
Herbie	46.3%

\[\begin{array}{l} \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if x < 1e-51

   1. Initial program 53.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   if 1e-51 < x

   1. Initial program 45.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Simplified 51.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)} \]
      Step-by-step derivation

      [Start] 45.7	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 45.7	\[ \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      +-commutative [=>] 45.7	\[ \color{blue}{\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 45.7	\[ \left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right)\right) - \left(j \cdot 27\right) \cdot k \]
      associate-+l+ [=>] 45.7	\[ \left(\left(-\left(x \cdot 4\right) \cdot i\right) + \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)}\right) - \left(j \cdot 27\right) \cdot k \]
      associate-+r+ [=>] 45.7	\[ \color{blue}{\left(\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) + \left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]
      associate--l+ [=>] 45.7	\[ \color{blue}{\left(\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right)} \]
      +-commutative [<=] 45.7	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(x \cdot 4\right) \cdot i\right)\right)} + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right) \]
      sub-neg [<=] 45.7	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(x \cdot 4\right) \cdot i\right)} + \left(\left(\left(-\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{-51}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, k \cdot \left(j \cdot -27\right)\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	45.9%
Cost	16068

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+289}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), b \cdot c + -27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	45.9%
Cost	9092

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq 4 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-j, 27 \cdot k, i \cdot \left(x \cdot -4\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	45.9%
Cost	3652

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t_2 \leq 4 \cdot 10^{+306}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) - t_1\\ \end{array} \]

Alternative 4
Accuracy	42.3%
Cost	2768

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := \left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - t_2\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-317}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-132}:\\ \;\;\;\;b \cdot c + \left(t_1 + x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 10^{-60}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) - t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-50}:\\ \;\;\;\;b \cdot c + \left(t_1 + x \cdot \left(y \cdot \left(t \cdot \left(18 \cdot z\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Accuracy	36.9%
Cost	2512

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ t_3 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;t_1 \leq -1000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-132}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) - t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+86}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	28.8%
Cost	2256

\[\begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(t \cdot a\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+37}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) - t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{-62}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - t_2\\ \end{array} \]

Alternative 7
Accuracy	28.6%
Cost	2256

\[\begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(t \cdot a\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+37}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) - t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - t_2\\ \end{array} \]

Alternative 8
Accuracy	44.4%
Cost	1856

\[\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

Alternative 9
Accuracy	38.2%
Cost	1737

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -1000 \lor \neg \left(t_1 \leq 10^{-62}\right):\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \]

Alternative 10
Accuracy	36.4%
Cost	1608

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+142}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) - t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+137}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - t_1\\ \end{array} \]

Alternative 11
Accuracy	24.0%
Cost	1499

\[\begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+156} \lor \neg \left(t \leq -1.4 \cdot 10^{+63}\right) \land \left(t \leq -1.12 \cdot 10^{+18} \lor \neg \left(t \leq 7.8 \cdot 10^{-194}\right) \land \left(t \leq 6.4 \cdot 10^{+102} \lor \neg \left(t \leq 3.3 \cdot 10^{+234}\right)\right)\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 12
Accuracy	24.8%
Cost	1364

\[\begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(t \cdot a\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := i \cdot \left(x \cdot -4\right) - t_2\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-197}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 4.25 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - t_2\\ \end{array} \]

Alternative 13
Accuracy	42.3%
Cost	1216

\[\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k \]

Alternative 14
Accuracy	14.3%
Cost	1112

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;i \leq -2.4 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-269}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;i \leq 0.052:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{+217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 15
Accuracy	23.0%
Cost	840

\[\begin{array}{l} \mathbf{if}\;j \leq -7.8 \cdot 10^{+130}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{-207}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 16
Accuracy	16.8%
Cost	585

\[\begin{array}{l} \mathbf{if}\;j \leq -2 \cdot 10^{+93} \lor \neg \left(j \leq 4.3 \cdot 10^{-196}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 17
Accuracy	16.8%
Cost	584

\[\begin{array}{l} \mathbf{if}\;j \leq -2.15 \cdot 10^{+93}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 18
Accuracy	12.7%
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023157 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))